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Resulting distribution of sample means

Rolling a fair twelve-sided die produces a uniformly distributed set of numbers between 1 and 12 with a mean of 6.5 and a standard deviation of 3.452. Assume that n twelve-sided dice are rolled many times and the mean of the n outcomes is computed each time.

a. Find the mean and standard deviation of the resulting distribution of sample means for n-49.

The mean of the resulting distribution of sample means is?

The standard deviation of the distribution of sample means is?

b. Find the mean and standard deviation of the resulting distribution of sample means for n = 121.

The mean of the resulting distribution of sample means is?

The standard deviation of the distribution of sample means is?

c. Why is the standard deviation in part a different from the standard deviation in part b?

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## Q : Discrete or continuous random variable

When rolling a die, is this an example of a discrete or continuous random variable? Explain your reasoning.